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Simulation and numerical approximation of semilinear stochastic PDEs

Abstract:

We are concerned with the simulation and numerical approximation of a variant of the Nagumo equation, which is perturbed by a Wiener process. In the first part of the talk we focus on the properties and the simulation of the Wiener noise. Then we discuss two possible ways in which the noise enters the reaction diffusion equation: external perturbations, which result in a stochastic PDE with additive noise, or perturbations of the reaction rate, which give a stochastic PDE with multiplicative noise. In both cases the presence of the noise induces interesting new phenomena to the system: For instance, we observe the nucleation of a new wave front or fluctuations of the wave speed. The last part of the talk gives a brief overview of the underlying numerical analysis.